Cost-effective Inspection and Maintenance Rule for Train Control Beacons

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Published Jul 3, 2026
Dersin Pierre Maxime Lousth

Abstract

A substantial part of the French railway network is equipped with ground-based beacons that control train speed. This
“KVB” system (French initials for beacon-based speed control) plays an important role in ensuring train operation safety.
When a beacon is failed, maximum speed compliance over the section where failure occurred is potentially at risk. Therefore,
detecting failed beacons and replacing them in a timely manner but not too often is fundamental to guarantee safe operation of the network while keeping maintenance costs under control. This is accomplished by means of regular commercial trains which detect failed beacons (albeit imperfectly). Upon a number p of successive detections of the same beacon as failed by different trains over a certain period (typically one day), this beacon is signaled as failed to the maintenance control center and is replaced as soon as possible. The question therefore arises of optimizing the signaling rule, i.e., determining the best number p of apparent detections that should trigger a maintenance intervention. Three main contributions are reported in this paper: 1) Determination of steady-state operational availability as a function of the failure rate, the headway, the mean time to restore and the fault detection probability; 2) A method for the optimal choice of the number p in the signaling rule; 3) An algorithm for diagnosing whether a beacon or a train is defective, thereby reducing detection time and false positives. Several sensitivity analyses are also conducted, both of the availability and the total cost,
with respect to the various relevant parameters. Generalization to other train control systems, such as the European-wide
Pierre Dersin et al. This is an open-access article distributed under the terms of the Creative Commons Attribution 3.0 United States License, which permits unrestricted use, distribution, and reproduction in any medium, provided
the original author and source are credited. ETCS (European Train Control System) should be straightforward. To the authors’ knowledge, it is the first time that such algorithms for decision optimization under uncertainty are applied in the context of train control system maintenance.

How to Cite

Pierre, D., & Lousth, M. (2026). Cost-effective Inspection and Maintenance Rule for Train Control Beacons. PHM Society European Conference, 9(1), 1–13. https://doi.org/10.36001/phme.2026.v9i1.5013
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Keywords

availability, maintenance costs, failure detection, optimization, decision support.

References
Bertsekas, D. (2012). Dynamic programming and optimal control. Athena Scientific.

Bewick V. Cheek, J., L. Ball. (2004). Statistics review 13: Receiver operating characteristic curve. Critical Care, 8.

Cooper, G. F. (1990). The computational complexity of probabilistic inference using Bayesian belief networks. Artificial
Intelligence, 42(2–3), 393–405.

Ghahramani, Z., & Jordan, M. I. (1997). Factorial hidden markov models. Machine Learning, 1–31.
Koller, D., & Friedman, N. (2009). Probabilistic graphical models: Principles and techniques. MIT Press.

Kschischang, F. R., Frey, B. J., & Loeliger, H.-A. (2001). EUROPEAN CONFERENCE OF THE PROGNOSTICS AND HEALTH MANAGEMENT SOCIETY 2026. Factor graphs and the sum-product algorithm. IEEE Transactions on Information Theory, 47(2), 498–519.

Murphy, K. P., Weiss, Y., & Jordan, M. I. (1999). Loopy belief propagation for approximate inference: An empirical
study. In Proceedings of the fifteenth conference on uncertainty in artificial intelligence (pp. 467–475).

Pearl, J. (1988). Probabilistic reasoning in intelligent systems:Networks of plausible inference. Morgan Kaufmann.

Ross, S. (2010). Introduction to probability models. Elsevier. Sch¨on, W., Benso, J.-N., Larraufie, G., Mo¨ens, G., & Por´e,
J. (2019). Railway signalling and automation (Vol. 3). La Vie du Rail.13
Section
Technical Papers